2. Derive a formula to approximate S* s* f(x;y)dxdy yo xo Using Simpson's rule with x2 – xo = 2h , y2 – Yo = 2k.

Q: * t/3 Evaluate the integral S'(y cos x – 3) dydx. S x -

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Q: Use the Laplace transform to solve the initial value problem. (a) y" – y' – 6y = 2, y(0) = 1, y'(0)…

A: Laplace transform

Q: Consider the ODE dr 4t + 6/, x (0) = 1. dt Use Euler's method with h=0.5 to approximate the solution…

A:

Q: Let f(x, y,z) = x² sin y + y e², where x =t + 3,y = net-1 and z = In 2t. dL at t = 1 is: 1-2n O -12n…

A: Given, fx,y,z=x2siny+yez, where x=t+3,y=πet-1 and z=ln 2t.   The objective is to determine dfdt at…

Q: Let f(x, y,z) = x² sin y +y e, where x t +3,y = net-1 and z = In 2t. %3D at t = 1 is: dt O -12n O…

A:

Q: By using Laplace transform to solve the IVP: y" - 4y' +9y=t, with y(0) = 0 and y'(0) = 1 Then Y(s)…

A: Given IVP is  y"-4y'+9y=t ......(1) y(0)=0,y'(0)=1 .....(2) We fin Y(s).

Q: 1 1-xl-x²-y? Evaluate the integral S S [dz dx dy 0 0 0

A: We will evaluate the given integral in this question.

Q: Use Laplace transform to solve the partial differential equation: o'y dy +xt where y(x,0)= 0,…

A: Solution

Q: 2 3 Evaluate the integral f S(x² + y)dydx. 0 1

A: Here given two variables in Integration

Q: Use the Laplace transform to solve the initial value problem. 3. x' + 2y' - y = 1; 2x' + y = 0; x(0)…

A:

Q: Prove that m-l dx =0 m +n (し+x)" where m,n are both Positive

A:

Q: Q1) Suppose w = x = cos? t, y = sin? t, z = dw Evaluate at t = 3, by using the Chain Rule dt

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Q: y' - | y(T) dr = t, y(0) = 3

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Q: -2-3 Evaluate the integral o S Jy² 2y dx dy.

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Q: Evaluate the double integral: ∬ 4y/(1+x2)dydx y runs from 1/2 to 2 x runs from 0 to 1

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Q: Use Laplace transforms to solve the initial value problem x'=x+2y, y'=x+e^-t; x(0)=y(0)=0

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Q: 2(3) Calculate the following commutators: (a) [d/dx, x·d/dx] (b) [sin(x), cos(x)] (c) [x^2, Ĥ] ,…

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Q: (a) Evaluate the integral ſ x e2x çdx (2x+1)²

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Q: The DE (xy - 4x') – x²y = 0 is dx Select one: O a. Homogeneous and Bernoulli. O b. Nonhomogenous and…

A:

Q: 1. Evaluate the given integral Q. -2 2y-2 -K² Q Jo 1 = (xy-1) dx dy

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Q: Use the Laplace transform to solve the given initial-value problem. y' + 5y = e4t, y(0) = 2 %3D y(t)…

A:

Q: use the Laplace transform to solve the given initial-value problem. Q y′−y =5sin2 t, y(0)=−1.

A: Given Data The differential equation is y’-y=5sin2t. y(0)=-1.   Using Laplace transform on the given…

Q: Use the Laplace transform to solve the given initial-value problem. y' + 5y = e3t, y(0) = 2 y(t) %3D

A:

Q: Use Laplace transforms to solve the following initial value problem. y" – yf – 6y = 0; y(0) = 1 ,…

A: The given IVP is as follows. y''-y'-6y=0; y0=1, y'0=-1 Apply Laplace transform on the IVP as…

Q: Find the approximate solution of the Poisson equation uxx + Uyy = -1 , Ix| s 1, lyl < 1 u = 0 at x =…

A:

Q: Find for x = x(t) defined implicitly by 25+25 x In(t) = e25xt Also evaluate dt at (t, x) = (1,1).

A: Given,25 + 25xlnt = e25xtTaking 'log' with base 'e' on both side, we getln25 + 25xlnt = lne25xtln25…

Q: Use Laplace transform to solve the partial differential equation: dy dy -+xt where y(x,0) = 0,…

A: Solution

Q: Use Euler's explicit method to solve the ODE dy/dx = 2.3y + 4e^−0.2x from x = 0 to x = 3 with the…

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Q: Solve the initial value problem using Laplace Transform: y" + 2ty' – 4y = 1, y(0) = y'(0) = 0 %3D

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Q: х-2 Evaluate the integral S (t3 In ti+ 3t3 sin (t*) j+ k) dt. x(x+1)

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Q: 15. Evaluate the line integral J. (3xy* - 6xy ]dx + (4x'y - 3x) dy, where C is any path from (1, 2)…

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Q: Solve the initial value problem using Laplace transform: x" + 25x = f(t), 5, 01

A: NOTE: Refresh your page if you can't see any equations. .

Q: 3. Using Laplace transform, find the solution of conditions y(0)=3 & y'(0)=1. d²y dt² +2y = cos 2t,…

A: Given d2ydt2+2y=cos2t with initial condition y0=3, y'0=1

Q: Use the Laplace transform to solve the given initial value problem. y" - 2y' + 2y = cos t; y(0) = 1,…

A: The differential equation is given as : y''-2y'+2y=cos ty(0)=1y'(0)=0 The objective is to find the…

Q: Use Laplace transform to solve the initial value problem y" – 2y' +y = e", y(0) = 0, y (0) = 0. %3D

A: Given problem :

Q: Solve the initial value problem using Laplace Transforms. x" - 3x' + 2x = t; x(0) = x'(0) = 0 %3D

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Q: d?y = v2sin/2t; with y(0) = 10, y(1)(0) = 0 %3D dt2

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Q: SSS zdV Q3: Evaluate E + y² + z² = 1 and x² + y² + z² = 4 in the upper where E lies between the…

A: We have to evaluate the integral ∭EzdV, where E lies between the spheres x2+y2+z2=1 and x2+y2+z2=4…

Q: dz a²z and 1 a) Find- Usin chain rule. If z = e*y – Sin xy, x=-, y=t? дх ду dt

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Q: 3 5. Evaluate the iterated integral: S x(x² + y)'/² dx dy.

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Q: Use Laplace transforms to solve the following initial value problem. x'+2y'+x=0, x'-y'+y=0, x(0)=0,…

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Q: Show that the solution y(t) of the initial value problem has the Laplace Transform y" + 2y' - 3y = 6…

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Q: Use Laplace transform to solve the partial differential equation: dy dy +xt where y(x,0)= 0,…

A: Solution

Q: Use the Laplace transform to solve the given initial-value problem. 1 y" +y= o(t-) + 이(t-), y(0)=0,…

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Q: O Evaluate the path integral between the points A = (1,3) and B = (2,5) of: (x²y + 2y)dy, with y =…

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Q: 2 Let z=x ·sin(y) 2 X=S •t y= st. dz Compute & in two ways: (i) Using the chain rule and S ô t (ii)…

A: Given that , z=x2siny where x=s2t , y=st find ∂z∂s , ∂z∂t

Q: 3t e"dt 2 (1+4e3

A: Let's integrate.

Q: Find any value of c for which the improper integral cx + 36 x2 + 1 9. da x (4 x + 5) converges.

A:

Q: se Euler method to compute ys for the DE yy'=2 x for y(1)=3

A: Euler's Method

Q: Q1) Suppose w =÷+ ?, x = cos² t, y = sin² t, z = ; Evaluate dw at t = 3, by using the Chain Rule dt

A:

Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.